The purpose of calculating significant figures is to express the precision and accuracy of a measurement or calculation. Significant figures represent the number of digits that are known with certainty, and they help ensure that the resulting value is not more precise than the original data.
In a calculation, the number of significant figures is determined by the number with the fewest significant figures. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures.
The scientific notation (10^4 and 10^-6) in this calculation represents the magnitude of the numbers being multiplied. It allows for easier representation and comparison of very large or very small numbers. It also helps maintain the correct number of significant figures in the final result.
The numbers 11.13 and 2.6 each have three significant figures, while 103.05 and 16.9 each have five significant figures. When performing calculations, it is important to keep track of the significant figures in each number to ensure the accuracy and precision of the final result.
The final result of the calculation is 1.44*10^5. To maintain the correct number of significant figures, the result should be rounded to three significant figures, since 11.13 has the fewest significant figures in the calculation. Therefore, the final result is 1.44*10^5, or 144,000.